Evaluate the definite integral. $\int^{12}_{6}6e^x\,dx = $ Choose 1 answer: Choose 1 answer: (Choice A) A $6e^{12}-6e^6$ (Choice B) B $\dfrac{e^{12}}{2}-e^6$ (Choice C) C $72e^{12}-36e^6$ (Choice D) D None of the above
Explanation: First, use the exponent rule: $\begin{aligned}\int^{12}_{6}6e^x\,dx =~6e^x\Bigg|^{12}_{{6}}\end{aligned}$ Second, plug in the limits of integration: $(6e^{{12}})-(6e^{{6}}) = 6(e^{12}-e^6)$. The answer: $\int^{12}_{6}6e^x\,dx~=~6e^{12}-6e^6$